A pentagon has a perimeter of 49 cm. The first and third sides are the same. The second side is 2 less than the first. The fourth side is 3 cm more than the first. The fifth side is twice the first. Find the length of each side.

Slide 3:

Let x = first side x-2 = second side x = third side x + 3 = fourth side 2x = fifth side x + (x – 2) + x + (x + 3) + 2x = 49 6x + 1 = 49 -1 -1 6x = 48 x = 8 So the sides are: 8 cm, 6 cm, 8 cm, 11 cm, and 16 cm

Slide 4:

Find the dimensions of a triangle whose sides are consecutive even integers and whose perimeter is 36.

Slide 5:

Let x = 1 st side x + 2 = 2 nd side x + 4 = 3 rd side x x+2 x + 4 3x + 6 = 36 -6 -6 3x = 30 3 3 x = 10 So the sides are: 10, 12, and 14

Slide 6:

John’s age is 6 more than twice the age of his twin sons. The sum of all their ages is 70. Find each person’s age.

Slide 7:

Let x = one twin’s age x = other twin’s age 2x + 6 = John’s age x + x + 2x + 6 = 70 4x + 6 = 70 -6 -6 4x = 64 x = 16 So the twins are 16 and John/Dad is 2(16) + 6 = 32 + 6 = 38.

Slide 8:

Find three consecutive odd integers such that 5 times the largest is 10 more than 7 times the smallest.

Slide 9:

Let x = 1 st CI X + 1 = 2 nd CI x + 2 = 3 rd CI 5(x + 4) = 7x + 10 5x + 20 = 7x + 10 -5x -5x 20 = 2x + 10 -10 -10 10 = 2x 5 = x So the numbers are 5, 7, and 9. Common sense check: 5(9) = 45 = 7(5) + 10 = 25 + 10 = 45

Slide 10:

The sum of 2 more than a certain number and three times the number is equal to the product of 2 and the sum of the number and 17. Find the number.

Slide 11:

Let x = THE number (x + 2) + (3x) = 2(x + 17) 4x + 2 = 2x + 34 -2x -2x 2x + 2 = 34 -2 -2 2x = 32 x = 16

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